The newest poll in the gubernatorial race showed a much tighter contest than previous surveys as the campaign turns the corner into the final two week before the primary election.

According to a Suffolk University-Boston Herald poll, Attorney General Martha Coakley holds a 12-point lead over Grossman with 42 percent of the vote to Grossman's 30 percent among very likely Democratic voters. Health care administrator Donald Berwick trails in third place with 16 percent, while 12 percent of likely Democratic primary voters are still undecided.

The poll, conducted Aug. 21 through Aug. 24, had a 4.9 percent margin of error.

The last SocialSphere/Boston Globe poll released last week had Coakley winning by a 21 point margin. The margin in the Globe poll shrunk to 18 points among voters who definitely plan to vote on Sept. 9. While Coakley held a commanding lead over Grossman among women (49 percent to 26 percent) in the Suffolk poll, she trailed the treasurer by a point among likely male voters in the Democratic primary. More than 13 percent of likely Democratic voters said they would vote for either the Republican nominee or an independent if their preferred candidate losses the Democratic primary, with 7.5 percent saying they would vote for the Republican and 5.75 percent saying they would vote for one of the three non-party candidates on the ballot in November.

The Suffolk poll also showed former state Sen. Warren Tolman holding a 6-point lead over former assistant attorney general Maura Healey in the Democratic race for attorney general, while former Brookline Selectwoman Deb Goldberg leads the primary race for treasurer with 20 percent. Goldberg's nearest rival in the three-way race for treasurer is state Sen. Barry Finegold at 8 percent, with Rep. Thomas Conroy in third at 7 percent.

Also, the three-way race for lieutenant governor is a toss-up with the three Democrats - Stephen Kerrigan, Mike Lake, and Leland Cheung - essentially splitting the small percentage (29 percent) of voters that have made up their minds in the race. On the Republican side of the ballot, expected nominee Charlie Baker holds a commanding lead over political novice Mark Fisher with 70 percent of likely GOP voters to Fisher's 11 percent.